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Instructor’s Solutions Manual
for
Numerical Analysis
9th EDITION
Richard L. Burden
Youngstown State University
J. Douglas Faires
Youngstown State University
Prepared by
Richard L. Burden
Youngstown State University
J. Douglas Faires
Youngstown State University
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
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© 2011 Brooks/Cole, Cengage Learning ISBN-13: 978-0-538-73596-4
ISBN-10: 0-538-73596-1
ALL RIGHTS RESERVED. No part of this work covered by the
copyright herein may be reproduced, transmitted, stored, or Brooks/Cole
used in any form or by any means graphic, electronic, or 20 Channel Center Street
mechanical, including but not limited to photocopying, Boston, MA 02210
recording, scanning, digitizing, taping, Web distribution, USA
information networks, or information storage and retrieval
systems, except as permitted under Section 107 or 108 of the Cengage Learning is a leading provider of customized
1976 United States Copyright Act, without the prior written learning solutions with office locations around the globe,
permission of the publisher except as may be permitted by the including Singapore, the United Kingdom, Australia,
license terms below. Mexico, Brazil, and Japan. Locate your local office at:
international.cengage.com/region
Cengage Learning products are represented in
For product information and technology assistance, contact us at Canada by Nelson Education, Ltd.
Cengage Learning Customer & Sales Support,
1-800-354-9706 For your course and learning solutions, visit
academic.cengage.com
For permission to use material from this text or product, submit
all requests online at www.cengage.com/permissions Purchase any of our products at your local college
Further permissions questions can be emailed to store or at our preferred online store
www.ichapters.com
NOTE: UNDER NO CIRCUMSTANCES MAY THIS MATERIAL OR ANY PORTION THEREOF BE SOLD, LICENSED, AUCTIONED,
OR OTHERWISE REDISTRIBUTED EXCEPT AS MAY BE PERMITTED BY THE LICENSE TERMS HEREIN.
READ IMPORTANT LICENSE INFORMATION
Dear Professor or Other Supplement Recipient: may not copy or distribute any portion of the Supplement to any
third party. You may not sell, license, auction, or otherwise
Cengage Learning has provided you with this product (the redistribute the Supplement in any form. We ask that you take
“Supplement”) for your review and, to the extent that you adopt reasonable steps to protect the Supplement from unauthorized
the associated textbook for use in connection with your course use, reproduction, or distribution. Your use of the Supplement
(the “Course”), you and your students who purchase the indicates your acceptance of the conditions set forth in this
textbook may use the Supplement as described below. Cengage Agreement. If you do not accept these conditions, you must
Learning has established these use limitations in response to return the Supplement unused within 30 days of receipt.
concerns raised by authors, professors, and other users
regarding the pedagogical problems stemming from unlimited All rights (including without limitation, copyrights, patents, and
distribution of Supplements. trade secrets) in the Supplement are and will remain the sole and
exclusive property of Cengage Learning and/or its licensors. The
Cengage Learning hereby grants you a nontransferable license Supplement is furnished by Cengage Learning on an “as is” basis
to use the Supplement in connection with the Course, subject to without any warranties, express or implied. This Agreement will
the following conditions. The Supplement is for your personal, be governed by and construed pursuant to the laws of the State
noncommercial use only and may not be reproduced, posted of New York, without regard to such State’s conflict of law rules.
electronically or distributed, except that portions of the
Supplement may be provided to your students IN PRINT FORM Thank you for your assistance in helping to safeguard the integrity
ONLY in connection with your instruction of the Course, so long of the content contained in this Supplement. We trust you find the
as such students are advised that they Supplement a useful teaching tool.
Printed in the United States of America
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Table of Contents
Preface vii
Mathematical Preliminaries 1
Exercise Set 1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Exercise Set 1.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Exercise Set 1.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Solutions of Equations of One Variable 19
Exercise Set 2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Exercise Set 2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Exercise Set 2.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Exercise Set 2.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Exercise Set 2.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Exercise Set 2.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Interpolation and Polynomial Approximation 41
Exercise Set 3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Exercise Set 3.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Exercise Set 3.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Exercise Set 3.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Exercise Set 3.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Exercise Set 3.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Numerical Differentiation and Integration 71
Exercise Set 4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Exercise Set 4.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Exercise Set 4.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Exercise Set 4.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Exercise Set 4.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Exercise Set 4.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Exercise Set 4.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Exercise Set 4.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Exercise Set 4.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
iii
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Instructor’s Solutions Manual
for
Numerical Analysis
9th EDITION
Richard L. Burden
Youngstown State University
J. Douglas Faires
Youngstown State University
Prepared by
Richard L. Burden
Youngstown State University
J. Douglas Faires
Youngstown State University
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
aires numerical
Burdenfaires
analysis
numerical
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instructors
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© 2011 Brooks/Cole, Cengage Learning ISBN-13: 978-0-538-73596-4
ISBN-10: 0-538-73596-1
ALL RIGHTS RESERVED. No part of this work covered by the
copyright herein may be reproduced, transmitted, stored, or Brooks/Cole
used in any form or by any means graphic, electronic, or 20 Channel Center Street
mechanical, including but not limited to photocopying, Boston, MA 02210
recording, scanning, digitizing, taping, Web distribution, USA
information networks, or information storage and retrieval
systems, except as permitted under Section 107 or 108 of the Cengage Learning is a leading provider of customized
1976 United States Copyright Act, without the prior written learning solutions with office locations around the globe,
permission of the publisher except as may be permitted by the including Singapore, the United Kingdom, Australia,
license terms below. Mexico, Brazil, and Japan. Locate your local office at:
international.cengage.com/region
Cengage Learning products are represented in
For product information and technology assistance, contact us at Canada by Nelson Education, Ltd.
Cengage Learning Customer & Sales Support,
1-800-354-9706 For your course and learning solutions, visit
academic.cengage.com
For permission to use material from this text or product, submit
all requests online at www.cengage.com/permissions Purchase any of our products at your local college
Further permissions questions can be emailed to store or at our preferred online store
www.ichapters.com
NOTE: UNDER NO CIRCUMSTANCES MAY THIS MATERIAL OR ANY PORTION THEREOF BE SOLD, LICENSED, AUCTIONED,
OR OTHERWISE REDISTRIBUTED EXCEPT AS MAY BE PERMITTED BY THE LICENSE TERMS HEREIN.
READ IMPORTANT LICENSE INFORMATION
Dear Professor or Other Supplement Recipient: may not copy or distribute any portion of the Supplement to any
third party. You may not sell, license, auction, or otherwise
Cengage Learning has provided you with this product (the redistribute the Supplement in any form. We ask that you take
“Supplement”) for your review and, to the extent that you adopt reasonable steps to protect the Supplement from unauthorized
the associated textbook for use in connection with your course use, reproduction, or distribution. Your use of the Supplement
(the “Course”), you and your students who purchase the indicates your acceptance of the conditions set forth in this
textbook may use the Supplement as described below. Cengage Agreement. If you do not accept these conditions, you must
Learning has established these use limitations in response to return the Supplement unused within 30 days of receipt.
concerns raised by authors, professors, and other users
regarding the pedagogical problems stemming from unlimited All rights (including without limitation, copyrights, patents, and
distribution of Supplements. trade secrets) in the Supplement are and will remain the sole and
exclusive property of Cengage Learning and/or its licensors. The
Cengage Learning hereby grants you a nontransferable license Supplement is furnished by Cengage Learning on an “as is” basis
to use the Supplement in connection with the Course, subject to without any warranties, express or implied. This Agreement will
the following conditions. The Supplement is for your personal, be governed by and construed pursuant to the laws of the State
noncommercial use only and may not be reproduced, posted of New York, without regard to such State’s conflict of law rules.
electronically or distributed, except that portions of the
Supplement may be provided to your students IN PRINT FORM Thank you for your assistance in helping to safeguard the integrity
ONLY in connection with your instruction of the Course, so long of the content contained in this Supplement. We trust you find the
as such students are advised that they Supplement a useful teaching tool.
Printed in the United States of America
1 2 3 4 5 6 7 11 10 09 08 07
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Table of Contents
Preface vii
Mathematical Preliminaries 1
Exercise Set 1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Exercise Set 1.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Exercise Set 1.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Solutions of Equations of One Variable 19
Exercise Set 2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Exercise Set 2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Exercise Set 2.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Exercise Set 2.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Exercise Set 2.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Exercise Set 2.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Interpolation and Polynomial Approximation 41
Exercise Set 3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Exercise Set 3.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Exercise Set 3.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Exercise Set 3.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Exercise Set 3.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Exercise Set 3.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Numerical Differentiation and Integration 71
Exercise Set 4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Exercise Set 4.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Exercise Set 4.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Exercise Set 4.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Exercise Set 4.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Exercise Set 4.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Exercise Set 4.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Exercise Set 4.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Exercise Set 4.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
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